Pierre André Chiappori (Columbia) "Family Economics" - Cemmap

9. Investment in Schooling and the Marriage Market 395
the externality argument. But the logic of competitive matching requires
the three aspects to be considered - and the unambiguous conclusion is
that efficiency is restored.
Finally, what about the opposite line of argument, according to which
agents actually invest too much? The story goes as follows: since agents
compete for the best spouse, a ‘rat race’ situation follows, whereby all
males overinvest in human capital. Well, again, the argument is incorrect in
a matching setting in which transfers are feasible between spouses. Indeed,
one should take into account not only the ‘quality’ (here the wealth) of
the spouse who will be attracted by a higher second period wealth, but
also the ‘price’ that will have to be paid (in terms of surplus sharing). In
a matching game, wealthier spouses come with a higher reservation utility,
thus require giving up a larger fraction of the surplus; as illustrated by the
previous example, this is exactly sufficient to induce the right investment
level. An important remark, however, is that this conclusion would not hold
in a Gale-Shapley framework, in which transfers are not possible and the
spouses’ respective gains are exogenously determined (and do not respond
to competitive pressures on the marriage market). In such a setting, the
‘rat race’ effect is much more likely to occur!
The model developed in this chapter assumes a large competitive marriage
market without frictions and we shall demonstrate that premarital
investments in schooling are efficient.
9.2 The Basic Model
We begin with a benchmark model in which men and women are completely
symmetric in their preferences and opportunities. However, by investing in
schooling, agents can influence their marriage prospects and labor market
opportunities. Competition over mates determines the assignment (that
is, who marries whom) and the shares in the marital surplus of men and
womenwithdifferent levels of schooling, depending on the aggregate number
of women and men that acquire schooling. In turn, these shares together
with the known market wages guide the individual decisions to invest in
schooling and to marry. We investigate the rational-expectations equilibrium
that arises under such circumstances.
9.2.1 Definitions
When man i and woman j form a union, they generate some aggregate
material output ζ ij that they can divide between them and the utility of
each partner is linear in the share he\she receives (transferable utility).
Man i alone can produce ζ i0 and woman j alone can produce ζ 0j. The